| """
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| Threshold Network for AND Gate
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|
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| A formally verified single-neuron threshold network computing logical conjunction.
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| Weights are integer-constrained and activation uses the Heaviside step function.
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| """
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|
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| import torch
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| from safetensors.torch import load_file
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|
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| class ThresholdAND:
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| """
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| AND gate implemented as a threshold neuron.
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|
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| Circuit: output = (w1*x1 + w2*x2 + bias >= 0)
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| With weights=[1,1], bias=-2: only (1,1) reaches threshold.
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| """
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|
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| def __init__(self, weights_dict):
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| self.weight = weights_dict['weight']
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| self.bias = weights_dict['bias']
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|
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| def __call__(self, x1, x2):
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| inputs = torch.tensor([float(x1), float(x2)])
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| weighted_sum = (inputs * self.weight).sum() + self.bias
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| return (weighted_sum >= 0).float()
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|
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| @classmethod
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| def from_safetensors(cls, path="model.safetensors"):
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| return cls(load_file(path))
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|
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| def forward(x, weights):
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| """
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| Forward pass with Heaviside activation.
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|
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| Args:
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| x: Input tensor of shape [..., 2]
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| weights: Dict with 'weight' and 'bias' tensors
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|
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| Returns:
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| AND(x[0], x[1])
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| """
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| x = torch.as_tensor(x, dtype=torch.float32)
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| weighted_sum = (x * weights['weight']).sum(dim=-1) + weights['bias']
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| return (weighted_sum >= 0).float()
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| if __name__ == "__main__":
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| weights = load_file("model.safetensors")
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| model = ThresholdAND(weights)
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|
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| print("AND Gate Truth Table:")
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| print("-" * 25)
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| for x1 in [0, 1]:
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| for x2 in [0, 1]:
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| out = int(model(x1, x2).item())
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| expected = x1 & x2
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| status = "OK" if out == expected else "FAIL"
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| print(f"AND({x1}, {x2}) = {out} [{status}]")
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|
